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844 JOURNAL OF SOFTWARE, VOL. 6, NO. 5, MAY 2011 completely, quote the case directly and make a conclusion. (b) Modifying It takes fault phenomenon vector as input and to reason with explained distance discrimination rules and past fault data. The reasoning machine issued a diagnostic probability order table of diagnosis result according to discrimination analysis rules, where the fault with maximum probability is the preferred result, and others are options by decreasing order of probability. If the case is not matched completely, The diagnostic probability order table will be available to maintenance personnel for reference of further confirm, use the Distance determination rule database, parts fault characteristic and actions record [16] etc. to Reasoning, adjust, rewrite, match and synthesize the case which has been retrieved according to the current fault phenomenon of equipment. (c) Storing Make the corrected case in keeping with the diagnosis of the current fault phenomenon, and make a conclusion. At the same time, the confirmed result will be fed back to fault database for record to prepare for the next diagnostic reference. The distance discrimination was used to fault diagnosis to establish expert system based on fault phenomenon vector. The core of fault diagnosis is that it can memorize/store the former fault, its environments and the process accurately, furthermore, it uses the past diagnosis experience, process and methods to complete the current diagnosis through analogy and association while diagnosing. Therefore, fault diagnosis based on fault phenomenon vector is a kind of methods realized through analogy [17, 18], and its design mode is to utilize the past designed case directly instead of the summary of design experience. III. KEY TECHNIQUES A. Rule-Based Diagnostic Expert Systems In the rule-based systems, knowledge is represented in the form of production rules. A rule describes the action that should be taken if a symptom is observed. The empirical association between premises and conclusions in the knowledge base is their main characteristic. These associations describe cause-effect relationships to determine logical event chains that were used to represent the propagation of complex phenomena. The general architecture of these systems includes domain independent components such as the rule representation, the inference engine and the explanation system. Basic structure of a classical rule-based expert system is shown in Fig. 2. Expert diagnosis experiences suitably formatted consists the basis for the classical expert system approach. Fault diagnosis requires domain specific knowledge formatted in a suitable knowledge representation scheme and an appropriate interface for the human-computer dialogue. In this system the possible symptoms of faults are presented to the user in a screen where the user can click the specific symptom in order to start a searching © 2011 ACADEMY PUBLISHER Fault database Knowledge base Distance determination rule database User interface maintenance personnel Inference engine Expert Figure 2. Basic structure of a rule-based expert system. process for the cause of the fault. Additional information about checking or measurements is used as input that, in combination with stored knowledge in the knowledge base guide to a conclusion [19, 20, 21, 23]. B. Reasoning Rules Formulation The formulation of rules needs to resolve problem of fault data table design. Table 1 is the designed fault data table of F1, where each line represents a fault phenomenon vector. Using the above method, we can build fault data table for each Fi. Each fault phenomenon obeys standard 0-1 distribution, the value of which is shown in (1). The expectation of each phenomenon is pij, where i represent that the phenomenon is caused by the i-th fault; j F1 TABLE I. DATA TABLE OF F1 Phenomenon Number I1 I2 I3 I4 … Im 1 1 0 0 1 … 1 2 1 0 1 0 … 0 3 0 0 1 1 … 0 4 1 0 1 0 … 0 5 1 0 1 1 … 0 6 1 0 1 0 … 0 7 1 0 1 1 … 0 8 0 0 0 1 … 0 9 1 0 0 0 … 0 10 1 1 1 0 … 0 … … … … … … … Total 1000 913 11 946 583 … 50
JOURNAL OF SOFTWARE, VOL. 6, NO. 5, MAY 2011 845 represents that this phenomenon is the j-th phenomenon in the set; N is the sample data amount of this fault; Iijt represents that the t-th fault phenomenon vector of fault i is caused by the j-th component. N ∑ I ijt * µ i = ( p ij ) j= 1, 2, � , m t= 1 = ( N ) j= 1, 2, �, m (1) The variance is as (2): 2 r = ( S ) i ij 1 = ( N −1 j= 1, 2, �, m N ∑( I ijt − t= 1 p ij ) 2 ) j= 1, 2, �, m Covariance between different phenomenons is as (3): ∑ = [ = [ σ ] i iuv u× v= m× m N ∑I iukI ivkP( Iiuk, Iivk ) ] u× v= m× m k= 1 ( iuk , ivk I I (2) (3) Where, P ) is the joint probability of two fault phenomenon, which has only four cases as (4): ⎧P( 0, 0) ⎪ P( 0, 1) P( I , I ) = ⎨ (4) iuk ivk ⎪ P( 1, 0) ⎪ ⎩ P( 1, 1) The research on woodworking machinery system fault phenomenon space arrived at conclusion that the emergency of each fault phenomenon subject to 0-1 independent and has the same distributions, That denoted as Ii1, Ii2 , . . . , Iin. With finite expected value * 2 µ i = E( Iij ) and finite variance σ i = D( Iij ) . Let Sn = Ii1 + Ii2 + … + Iin. 2 2 Sn σ i We know D( Sn ) = nσ i , D( ) = Also we n n S ∗ know that E( ) = µ n n . We know from the large number law,by chebyshev’s inequality, then for anyε > 0 , as (5): 2 ⎛ Sn * ⎞ σ i P⎜ − µ i ≥ ε ⎟ ≤ . (5) 2 ⎝ n ⎠ nε Thus, for fixed ε as (6): ⎛ Sn * ⎞ P ⎜ − µ i ⎟ ≥ ε → 0 (6) ⎝ n ⎠ As n → ∞ . Equivalently as (7): ⎛ Sn * ⎞ P ⎜ − µ i ⎟ < ε → 1. (7) ⎝ n ⎠ That when the number of sample goes to infinity, the expectation limit of samples is equal to that of the overall is shown in (5-7) and sample variance is equal to that of © 2011 ACADEMY PUBLISHER overall, the covariance of sample is equal to that of overall [22]. As Table 1 shows, the expectation of I1 caused by F1 is equal to p11=913/1000 =0.913. Furthermore, the * expectation fault phenomenon vector of fault Fi is µ i , which is the accumulation point according to probability distribution in the space of all fault phenomenon caused by Fi. The discrimination analysis idea indicates that * when perform distance discrimination of all µ i and fault phenomenon vector to be diagnosed, then the fault phenomenon vector is possible belong to the x-th space. That is the probability that it caused by the x-th is the largest. In this way, the order result from little to large will led to sort of diagnose probability descending. The distance here can be Euclidean distance as (8), or be Mahalanobis distance as (9): * i Dis = µ − µ i = ∑ ∞ j= 1 ( d − p ) j T i ij ∑ −1 * ( D − i i * Dis ( x, G) = ( D − ) µ ) i Where, ∑ −1 i (8) µ (9) is the inverse matrix of covariance matrix. The Euclidean distance is intuitive, while the Mahalanobis distance needs to compare and discriminate the standard overall phenomenon caused by each fault, so to as reflect reality. In the practical application, Mahalanobis distance needs to know the inverse matrix of covariance matrix among all phenomenon, which involve inverse operation, so it ie relatively complex. C. Design of Learning Strategy When the system is built, we should summarize expert diagnosis experience and input. The automatic learning in system running process can add conformed fault phenomenon vector into fault database. The sort according to probability from large to little will cause misdiagnosis, which means it may be wrong to take the fault at the most front as diagnosis result. The discrimination may cause mistakes, which is the fact that can not mastered by people. If the empirical data is very rich, the possibility of misdiagnosis will be very small. As to mistakes, the system will be the second diagnosis, which is ranked second in the probability of failure as a diagnostic output, and so on. The storage form affects the problem solving efficiency, whereas regulation and evaluation affect the problem solving accuracy. The matching degree of the fault and fault phenomenon can be expressed as (10): s n ∑ i= 1 2 D ( c, c′ ) = 1− W ( X −Y ) / n (10) i Where D s is the matching degree of fault c and fault phenomenon c′ ; W i is the weight of characteristic parameter i; n is the number of all symptoms; X i and i i
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Journal of Software ISSN 1796-217X
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